Environments such as commercial airliners frequently have several radios that operate at different frequencies. Not only must these radios avoid interference with each other, but also they must meet spectrum mask requirements imposed by regulatory agencies, such as the United States Federal Communications Commission. The output from the solid state power amplifier of such a radio often includes distortion that can be characterized by a hyperbolic tangent function. Both amplitude distortion and phase distortion may occur. The transmit spectrum of such a radio signal can spread near the desired signal band if the envelope of the transmitted signal is not constant, particularly if the transmitter power amplifier is being driven into soft saturation. While spurious emissions might be reduced by predistorting of the radio frequency signal envelope just before transmission to the output power amplifier, this requires analog multipliers. Even then, if noise is picked up in the multiplier circuit, that noise will modulate the desired signal and pass through to the output.
One approach to overcoming power amplifier nonlinearity utilizes the function f(x)=2x/(1+x2) for amplitude predistortion and the function ph(x)=(πf(x))/6=2πx/6(1+x2) for phase predistortion, where x is the instantaneous value of the envelope. Another approach to overcoming amplitude distortion is to utilize the “cuber” function f(x)=x+x3/3, where again x is the instantaneous value of the envelope. These approaches have been found to provide less than optimum linearity in the power amplifier output.